The use of two parameters fracture mechanics criterion as a tool for structural design and analysis has increased significantly in recent years. First, we discuse the elastic solution for the stress distribution at crack tip for two dimensional geometries and particularly constraint as T-stress under various loading conditions. Secondly, using notch fracture mechanics and particularly the Volumetric Method approach, we study the stress distribution at the tip of a notch in pipes submitted to internal pressure. The Notch Stress Intensity Factor Kρ and the effective T-stress are combined into a two-parameter fracture criterion (KIρ-Tef). This approach is then used to quantify the constraint of notch-tip fields for various pipe geometry and loading conditions.